Pruning should begin when the weather has gotten sufficiently cold for long enough for plants to drop their leaves and the plant sap to move down to the roots. Planning pruning once plants have gone dormant provides time for the wounds to heal before new growth starts in the spring.
However, be aware that some plants need to be pruned early in the winter, some later in the winter, some after spring blooms drop, and some not at all.
Shrubs such as evergreens, boxwoods, hollies, and privets can be trimmed in early winter to control their shape and remove unwanted branches. Larger shrubs like Rose of Sharon, Hardy Hibiscus, Crape Myrtle and Hardy Hydrangea can be pruned, but be aware that there are species of these common shrubs that flower in the Spring from old growth, not new growth. If your Crape Myrtle, for instance, flowers from new growth, pruning will not affect flowering. If you do not know, be sure to watch this spring to see where the blooms come from.
Shrub roses may be pruned while they are dormant to shape the plants and remove dead growth. Climbing roses will usually bloom on old growth so pruning will limit the amount of blooming in the spring and summer months.
Vines can be pruned to limit growth and open them up to allow more sunlight into the vines. Vines normally bloom on new growth so a light trim in the winter will not severely limit spring and summer flowering. Vines such as Jasmines, honeysuckles, and passionflowers can all be trimmed.
Trees including oaks, elms, and fruit trees should be pruned early in the winter while the temperatures are coldest. For these trees and others that bleed sap from wounds, early pruning allows for wounds to heal before pests and disease can get a foothold. Flowering trees should not be pruned until after their spring flowers drop.
Grasses and perennial flowers can be pruned back once they have gone dormant and the leaves have dried out. If there are seed heads you may consider leaving the seed heads to provide food for winter birds and do your heavy pruning in early spring.
Finally, there is no bad time to remove suckers from your plants, although winter is best. Some shrubs such as crape myrtle, forsythia, chaste trees, and willows will continually send up new growth from roots and the lower trunks. These can easily form a colony that drains nutrients from the parent plant and makes your plants very unsightly.
Once you have given thought to what and when to prune go to:
https://aggie-horticulture.tamu.edu/earthkind/landscape/proper-pruning-techniques/ to learn proper techniques for different plants.
by Rob Franks, ECMG